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## Surface Area and Volume of Spheres

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**12.6**Surface Area and Volume of Spheres**Sphere – Set of all point in space equidistant from a**given point. Center Radius – a segment from the center to a point on the sphere. Chord – A segment whose endpoints are on the sphere. Diameter – A chord that contain the center. Vocabulary**The surface area S of a sphere is**• S = 4 πr2 • Where r is the radius Surface Area**Find the surface area of the sphere.**ANSWER The surface area of the sphere is about 804.25square inches. EXAMPLE 1 Find the surface area of a sphere SOLUTION S = 4πr2 Formula for surface area of a sphere. = 4π(82) Substitute 8 for r. = 256π Simplify. ≈ 804.25 Use a calculator.**ANSWER**2.71 for Examples 1 and 2 GUIDED PRACTICE 2. The surface area of a sphere is 30π square meters. Find the radius of the sphere.**The diameter of the outer sphere is 12feet, so the**12 radius is = 6feet. 2 EXAMPLE 3 Use the circumference of a sphere EXTREME SPORTS In a sport called sphereing, a person rolls down a hill inside an inflatable ball surrounded by another ball. The diameter of the outer ball is 12feet. Find the surface area of the outer ball. SOLUTION**ANSWER**The surface area of the outer ball is 144π, or about 452.39 square feet. EXAMPLE 3 Use the circumference of a sphere Use the formula for the surface area of a sphere. S = 4πr2 = 4π(62) = 144π**Great Circle – a cross section of the sphere that contain**the center Hemisphere – one half of the circle created by the great circle cross section. Vocab**Approximate the volume**of the sphere as the sum of n pyramids each with a volume of V = (1/3)Bh. Volume**The diameter of the ball is 9 inches, so the radius is**= 4.5 inches. 9 2 4 V = πr3 3 4 = π(4.5)3 3 EXAMPLE 4 Find the volume of a sphere The soccer ball has a diameter of 9 inches. Find its volume. SOLUTION Formula for volume of a sphere Substitute.**ANSWER**The volume of the soccer ball is 121.5π, or about 381.70 cubic inches. Find the volume of a sphere EXAMPLE 4 = 121.5π Simplify. ≈ 381.70 Use a calculator.**Find the volume of the composite solid.**1 4 = πr2h – ( πr3) 2 3 2 = π(2)2(2) – π(2)3 3 2 = 8π – (8π) 3 Find the volume of a composite solid EXAMPLE 5 SOLUTION Formulas for volume Substitute. Multiply.**24**16 = π – π 3 3 8 = π 3 ANSWER 8 The volume of the solid is π, or about 8.38 cubic inches. 3 Find the volume of a composite solid EXAMPLE 5 Rewrite fractions using least common denominator. Simplify.**842-843**• 3-9 odd, 13,17,21-27 Homework